Lumps and P-branes in Open String Field Theory
R. de Mello Koch, A. Jevicki, M. Mihailescu, R. Tatar
TL;DR
This paper develops a numerical framework to construct lump solutions in open bosonic string field theory as realizations of lower-dimensional D$p$-branes and tests Sen's conjecture by comparing lump energies to brane tensions. It retains the exponential higher-derivative terms of the Witten vertex and uses level truncation to solve a nonlinear momentum-space integral equation for the tachyon field, implemented with a spherically symmetric ansatz and efficient Fourier-transform-based convolutions. The authors compute D$p$-brane tensions from the lump solutions and find good agreement with the expected tensions, providing evidence for Sen's conjecture and illustrating the utility of the Witten SFT formulation for nonperturbative solitons. The work highlights the importance of higher-derivative terms in off-shell dynamics and presents a viable numerical route for analyzing nonperturbative structures in string field theory.
Abstract
We describe numerical methods for constructing lump solutions in open string field theory. According to Sen, these lumps represent lower dimensional Dp-Branes and numerical evaluation of their energy can be compared with the expected value for the tension. We take particular care of all higher derivative terms inherent in Witten's version of open string field theory. The importance of these terms for off shell phenomena is argued in the text. Detailed numerical calculations done for the case of general $p$ brane show very good agreement with Sen's conjectured value. This gives credence to the conjecture itself and establishes further the usefulness of Witten's version of SFT .